Ebenbeck, Matthias and Knopf, Patrik (2020) Optimal control theory and advanced optimality conditions for a diffuse interface model of tumor growth. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 26: 71. ISSN 1292-8119, 1262-3377
Full text not available from this repository. (Request a copy)Abstract
We investigate a distributed optimal control problem for a diffuse interface model for tumor growth. The model consists of a Cahn-Hilliard type equation for the phase field variable, a reaction diffusion equation for the nutrient concentration and a Brinkman type equation for the velocity field. These PDEs are endowed with homogeneous Neumann boundary conditions for the phase field variable, the chemical potential and the nutrient as well as a "no-friction" boundary condition for the velocity. The control represents a medication by cytotoxic drugs and enters the phase field equation. The aim is to minimize a cost functional of standard tracking type that is designed to track the phase field variable during the time evolution and at some fixed final time. We show that our model satisfies the basics for calculus of variations and we present first-order and second-order conditions for local optimality. Moreover, we present a globality condition for critical controls and we show that the optimal control is unique on small time intervals.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CAHN-HILLIARD SYSTEM; OPTIMAL DISTRIBUTED CONTROL; DARCY MODEL; SIMULATION; CHEMOTAXIS; INVASION; Optimal control with PDEs; calculus of variations; tumor growth; Cahn-Hilliard equation; Brinkman equation; first-order necessary optimality conditions; second-order sufficient optimality conditions; uniqueness of globally optimal solutions |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 10 Mar 2021 13:29 |
| Last Modified: | 10 Mar 2021 13:29 |
| URI: | https://pred.uni-regensburg.de/id/eprint/43733 |
Actions (login required)
 |
View Item |
